The Equifax hack exposed the names, addresses, birthdates and Social Security numbers of up to 145.5 million Americans. Drivers license information for 10.9 million people was also exposed, according to a Wall Street Journal report.

This is the sensitive, private information that’s used to establish your identity, which is why freezing your credit reports — as important as that is — won’t be enough.

Within a day or two, you should get an activation code that allows you to sign up for one-bureau monitoring at Experian. Now, Experian’s a for-profit company, so it will try to sell you upgrades, such as a peek at “your credit score”–actually a PLUS score that isn’t used by lenders. You don’t have to buy anything or give up a credit card number to get the credit monitoring, however.

You will have to cough up your Social Security number and answer some questions culled from your credit report there so Experian will know you’re really you. As always, make sure the URL starts with an “https” before you give up private personal information.

You always need to be wary of credit monitoring offers. Apparently scamsters pretending to be Target are already targeting its customers, so you want to be sure you navigate to the right sites. Don’t click on links in random emails or give out private information over the phone to anyone who calls.

Another hazard has to do with lawsuits. Some companies offer credit monitoring after a breach, but in the fine print you agree to give up your rights to sue the company that suffered the breach or participate in class action lawsuit settlements.

In this case, the fine print requires you to agree to arbitration if there’s a problem with your credit monitoring service, but there’s no mention of giving up your rights regarding any future Target litigation.